Any large, urban county could fit under this criteria.
Cook, Los Angeles, and Dade Counties all have strong Republican areas despite being in very Democratic-voting counties.
The inverse is somewhat more difficult to find, but I'm guessing the resort areas of the Mountain West and the Appalachians would be good candidates.
The inverse is all over the place, there's a small urban core area in a lot of counties that has a few precincts that vote Dem while the rest of the county votes GOP. If not an urban core then there might be a small minority heavy area of the county that votes Dem too.
I know Grand Traverse County MI is a good example of this. Traverse City votes Dem which includes I think 3 precincts, but the remainder of the county votes GOP.
Hillary dropped off big in a lot of small towns, but Obama used to do well in them despite losing by decent margins in fully rural areas. In Kansas, for example, he won parts of Salina and Hutchinson (Hillary still won a few precincts) despite those cities being in heavily GOP counties. Often where there's a college this effect exists. Take Hays in Ellis County Kansas. The precinct that contains Fort Hays State is Democratic despite Ellis County being heavily Republican.
